What is the GCF of 78 and 82?

Solution: The GCF of 78 and 82 is 2

Methods

How to find the GCF of 78 and 82 using Prime Factorization

One way to find the GCF of 78 and 82 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:

Here is the prime factorization of 78:

2^1 × 3^1 × 13^1

And this is the prime factorization of 82:

2^1 × 41^1

When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 78 and 82 by multiplying all the matching prime factors to get a GCF of 78 and 82 as 4:

Thus, the GCF of 78 and 82 is: 4

How to Find the GCF of 78 and 82 by Listing All Common Factors

The first step to this method of finding the Greatest Common Factor of 78 and 82 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.

Let’s take a look at the factors for each of these numbers, 78 and 82:

Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78

Factors of 82: 1, 2, 41, 82

When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 78 and 82 would be 2.

Find the GCF of Other Number Pairs

Want more practice? Try some of these other GCF problems:

Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.

Get PDF

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.